100 500 2500 20 Given the series 9 81 729 6561 Does this series converge or diverge? O converges O diverges If the series converges, find the sum:

Q: Consider the conservative vector field F(r, y, z) = (2x, z, y). a) Determine a potential f such that...

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Q: 3. Determine whether The Mean Value Theorem ca be applied to f(x)= Vx+ 3 on |-3,6|. Find all value o...

A: The given function f(x)=x+3 on [-3,6]

Q: 6. (a) Describe the level curves of the function f(x,y) = y – sin x. (b) Describe the level surfaces...

A: Let's find. 

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: Discuss the continuity of the function: x² + 2x-4 x -2

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Q: Sin x y = 2+Cos x

A: Given, y=sinx2+cosx We have to find the derivative of the above function.  

Q: Solve the given differential equation x2y" + xy' – y = In x y(x) =

A: Given: x2y''+xy'-y=ln xAsnwer: y(x)=c1 x+c2x-ln xUsing Cauchy's Euler method:Substitute  x=et; x>...

Q: 1 if x is an integer Let f be the function defined by f(x) = { oif x is not an integer a.) Sketch th...

A: The given function,f(x)=1if x is an integer0if x is not an integer

Q: model of automobile

A: V(x)=25000-0.25x  Which is a linear equation with negative slope so from here we can say that as the...

Q: Solve the following DE, using Separable method. 1.50 point y'In ly+ x*y 0.

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Q: A company produces a special new type of TV. The company has fixed costs of $458,000, and it costs $...

A: Given that company has fixed costs of $458000 and it costs $1200 to produce each TV.Also the company...

Q: 1. Find all possible points of discontinuity and classify each discontinuity as removable, jump esse...

A: This is a limit and discontinuity problem

Q: 25/quizzes/3828 Spot the mistake/s in the solution. Tick the box that applies. S sin x n (cos ) dx %...

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Q: Example 8 Video Example ) Differentiate y = x7Vx. Solution 1 Since both the base and the exponent ar...

A: Given query is to find the derivative of the expression.

Q: For Nos. 9-10: Suppose f is a function such that f0(5) is undefined. Which of the following statemen...

A: Given that a function f is as follows  I.e f(5) is not defined  We know that  Any function is contin...

Q: F = 2 i +x j – k

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Q: 3. Sketch the graph of the derivative of the function below.

A: A rough graph can be plotted as values are not given in the given graph

Q: Consider the equation below. x2 + 9y – 9z? = 0 Reduce the equation to one of the standard forms. Cla...

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Q: 9. Reduce the following equation to one of the standard forms, classify the surface, then sketch the...

A: General equation of an ellipsoid is given by, (x-p)²/a² +(y-q)²/b² +(z-r)²/c²= 1

Q: dx x2 – 64 First, rewrite this with partial fractions: S, da = f 1/(x+8) dx + [ 1/(x-8) dr = log(x+8...

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Q: Solve the differential equation by variation of parameters. y" - y = cosh x y(x) II

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Q: Find f'(x). f(x) = e – x³ arctan(x) -(3 + 3x2 arctan(x) + arctan(x)(3x4)) x2 +1 f'(x)

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: Find all solutions of the equation in the interval 0, 2n). sine(2 cos 0 + /2) = 0

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Q: 00 Let S = an be an infinite series such that SN =5 6. N2 : %3D n=1 10 16 (a) What are the values of...

A: Given, SN=5-6N2

Q: Assume that a snowball is in the shape of a sphere. If a snowball melts so that its surface area dec...

A: topic - application of derivatives

Q: Consider the differential equation dy 1 dr? y3 A solution to the above equation is Select one:

A: Given :d2ydx2=1y3  

Q: 5. The depth of water in a port is modelled by the function d(t) = pcosqt + 7.5, for 0 <t < 12, wher...

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Q: Solve the given differential equation. x2y" + 13xy' + 36y = 0 y(x) = ,x > 0

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Q: S 3x f"(x) dx 48 42 36 NONE OF THE CHOICES о

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Q: Calculate the first four terms of the sequence, starting with n = 1. bị = -5 1 bn = bn-1 + bn–1 (Giv...

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Q: What is the slope of the given curve y = 8x

A: Give curve,         y = 8x-3x² at point (2,4)

Q: (x³-5x)* 1. y = ; d'y/dx³

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Q: (2) Find the exact trigonometric ratios for the angle r whose radian measure is given. 57 sin (z) =....

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Q: In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all directio...

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Q: Solve  (x+1)(dy/dx) +y = ln(x) y(1)=0

A: We will solve the differential equation. 

Q: Use the Integral Test to determine whether the infinite series 15 is convergent. (Use symbolic notat...

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Q: 5. Consider the graph of y = f(x) below. On the same set of axes sketch a clearly labelled graph of ...

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Q: Use the Integral Test to determine whether the infinite series is convergent. -n² 16ne n=4 Fill in t...

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Q: Find the tangent line to the curve y = 2x - x2 at (2,0)

A: The equation of the curve is given by y = 2x-x2 The point is x0, y0 = 2, 0 Formula Used: The formula...

Q: Find the equations of normal of the curve y = 2x-x-at (2, 0).

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Q: Find the exact value of: sin-1 (-) %3D %3D %3D 11

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Q: (3y²-x² ()y' -=0 ;when x = 1, y = 1 2y4

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Q: Evaluate the integral: 3 49x2dx

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Q: boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on...

A: topic - application of derivatives

Q: Find DE 576 || x9 Type your answer without fractional or negative exponents. Use sqrt(x) for sqrt(x)...

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Q: C. Without a table of values and without graphing f(x), give the values of the following limits. 21-...

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Q: Use the graph shown below and identify points from A through I that satisfy the given conditions. y ...

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Q: This problem concerns the elliptic cone. Consider the equation x²/a² + y²/b² – z²/c² = 0. (a) Descri...

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Q: When you evaluate: dx The sum of the coefficient of - for any constant n is A None of the given choi...

A: This is a basic integration problem